/***************************************************************************/
/*                                                                         */
/*  fttrigon.c                                                             */
/*                                                                         */
/*    FreeType trigonometric functions (body).                             */
/*                                                                         */
/*  Copyright 2001, 2002, 2003, 2004, 2005 by                              */
/*  David Turner, Robert Wilhelm, and Werner Lemberg.                      */
/*                                                                         */
/*  This file is part of the FreeType project, and may only be used,       */
/*  modified, and distributed under the terms of the FreeType project      */
/*  license, LICENSE.TXT.  By continuing to use, modify, or distribute     */
/*  this file you indicate that you have read the license and              */
/*  understand and accept it fully.                                        */
/*                                                                         */
/***************************************************************************/


#include <ft2build.h>
#include FT_INTERNAL_OBJECTS_H
#include FT_TRIGONOMETRY_H


/* the following is 0.2715717684432231 * 2^30 */
#define FT_TRIG_COSCALE 0x11616E8EUL

/* this table was generated for FT_PI = 180L << 16, i.e. degrees */
#define FT_TRIG_MAX_ITERS 23

static const FT_Fixed
ft_trig_arctan_table[24] =
{
    4157273L, 2949120L, 1740967L, 919879L, 466945L, 234379L, 117304L,
    58666L, 29335L, 14668L, 7334L, 3667L, 1833L, 917L, 458L, 229L, 115L,
    57L, 29L, 14L, 7L, 4L, 2L, 1L
};

/* the Cordic shrink factor, multiplied by 2^32 */
#define FT_TRIG_SCALE 1166391785UL     /* 0x4585BA38UL */


#ifdef FT_CONFIG_HAS_INT64

/* multiply a given value by the CORDIC shrink factor */
static FT_Fixed
ft_trig_downscale(FT_Fixed val)
{
    FT_Fixed s;
    FT_Int64 v;


    s = val;
    val = (val >= 0) ? val : -val;

    v = (val * (FT_Int64)FT_TRIG_SCALE) + 0x100000000UL;
    val = (FT_Fixed)(v >> 32);

    return (s >= 0) ? val : -val;
}

#else /* !FT_CONFIG_HAS_INT64 */

/* multiply a given value by the CORDIC shrink factor */
static FT_Fixed
ft_trig_downscale(FT_Fixed val)
{
    FT_Fixed s;
    FT_UInt32 v1, v2, k1, k2, hi, lo1, lo2, lo3;


    s = val;
    val = (val >= 0) ? val : -val;

    v1 = (FT_UInt32)val >> 16;
    v2 = (FT_UInt32)(val & 0xFFFFL);

    k1 = (FT_UInt32)FT_TRIG_SCALE >> 16;       /* constant */
    k2 = (FT_UInt32)(FT_TRIG_SCALE & 0xFFFFL);   /* constant */

    hi = k1 * v1;
    lo1 = k1 * v2 + k2 * v1;        /* can't overflow */

    lo2 = (k2 * v2) >> 16;
    lo3 = (lo1 >= lo2) ? lo1 : lo2;
    lo1 += lo2;

    hi += lo1 >> 16;
    if (lo1 < lo3)
        hi += (FT_UInt32)0x10000UL;

    val = (FT_Fixed)hi;

    return (s >= 0) ? val : -val;
}

#endif /* !FT_CONFIG_HAS_INT64 */


static FT_Int
ft_trig_prenorm(FT_Vector* vec)
{
    FT_Fixed x, y, z;
    FT_Int shift;


    x = vec->x;
    y = vec->y;

    z = ((x >= 0) ? x : -x) | ((y >= 0) ? y : -y);
    shift = 0;

    #if 1
    /* determine msb bit index in `shift' */
    if (z >= (1L << 16))
    {
        z >>= 16;
        shift += 16;
    }
    if (z >= (1L << 8))
    {
        z >>= 8;
        shift += 8;
    }
    if (z >= (1L << 4))
    {
        z >>= 4;
        shift += 4;
    }
    if (z >= (1L << 2))
    {
        z >>= 2;
        shift += 2;
    }
    if (z >= (1L << 1))
    {
        z >>= 1;
        shift += 1;
    }

    if (shift <= 27)
    {
        shift = 27 - shift;
        vec->x = x << shift;
        vec->y = y << shift;
    }
    else
    {
        shift -= 27;
        vec->x = x >> shift;
        vec->y = y >> shift;
        shift = -shift;
    }

    #else /* 0 */

    if (z < (1L << 27))
    {
        do
        {
            shift++;
            z <<= 1;
        }
        while (z < (1L << 27));
        vec->x = x << shift;
        vec->y = y << shift;
    }
    else if (z > (1L << 28))
    {
        do
        {
            shift++;
            z >>= 1;
        }
        while (z > (1L << 28));

        vec->x = x >> shift;
        vec->y = y >> shift;
        shift = -shift;
    }

    #endif /* 0 */

    return shift;
}


static void
ft_trig_pseudo_rotate(FT_Vector* vec,
                      FT_Angle theta)
{
    FT_Int i;
    FT_Fixed x, y, xtemp;
    const FT_Fixed* arctanptr;


    x = vec->x;
    y = vec->y;

    /* Get angle between -90 and 90 degrees */
    while (theta <= -FT_ANGLE_PI2)
    {
        x = -x;
        y = -y;
        theta += FT_ANGLE_PI;
    }

    while (theta > FT_ANGLE_PI2)
    {
        x = -x;
        y = -y;
        theta -= FT_ANGLE_PI;
    }

    /* Initial pseudorotation, with left shift */
    arctanptr = ft_trig_arctan_table;

    if (theta < 0)
    {
        xtemp = x + (y << 1);
        y = y - (x << 1);
        x = xtemp;
        theta += *arctanptr++;
    }
    else
    {
        xtemp = x - (y << 1);
        y = y + (x << 1);
        x = xtemp;
        theta -= *arctanptr++;
    }

    /* Subsequent pseudorotations, with right shifts */
    i = 0;
    do
    {
        if (theta < 0)
        {
            xtemp = x + (y >> i);
            y = y - (x >> i);
            x = xtemp;
            theta += *arctanptr++;
        }
        else
        {
            xtemp = x - (y >> i);
            y = y + (x >> i);
            x = xtemp;
            theta -= *arctanptr++;
        }
    }
    while (++i < FT_TRIG_MAX_ITERS);

    vec->x = x;
    vec->y = y;
}


static void
ft_trig_pseudo_polarize(FT_Vector* vec)
{
    FT_Fixed theta;
    FT_Fixed yi, i;
    FT_Fixed x, y;
    const FT_Fixed* arctanptr;


    x = vec->x;
    y = vec->y;

    /* Get the vector into the right half plane */
    theta = 0;
    if (x < 0)
    {
        x = -x;
        y = -y;
        theta = 2 * FT_ANGLE_PI2;
    }

    if (y > 0)
        theta = -theta;

    arctanptr = ft_trig_arctan_table;

    if (y < 0)
    {
        /* Rotate positive */
        yi = y + (x << 1);
        x = x - (y << 1);
        y = yi;
        theta -= *arctanptr++; /* Subtract angle */
    }
    else
    {
        /* Rotate negative */
        yi = y - (x << 1);
        x = x + (y << 1);
        y = yi;
        theta += *arctanptr++; /* Add angle */
    }

    i = 0;
    do
    {
        if (y < 0)
        {
            /* Rotate positive */
            yi = y + (x >> i);
            x = x - (y >> i);
            y = yi;
            theta -= *arctanptr++;
        }
        else
        {
            /* Rotate negative */
            yi = y - (x >> i);
            x = x + (y >> i);
            y = yi;
            theta += *arctanptr++;
        }
    }
    while (++i < FT_TRIG_MAX_ITERS);

    /* round theta */
    if (theta >= 0)
        theta = FT_PAD_ROUND(theta, 32);
    else
        theta = -FT_PAD_ROUND(-theta, 32);

    vec->x = x;
    vec->y = theta;
}


/* documentation is in fttrigon.h */

FT_EXPORT_DEF(FT_Fixed)
FT_Cos(FT_Angle angle)
{
    FT_Vector v;


    v.x = FT_TRIG_COSCALE >> 2;
    v.y = 0;
    ft_trig_pseudo_rotate(&v, angle);

    return v.x / (1 << 12);
}


/* documentation is in fttrigon.h */

FT_EXPORT_DEF(FT_Fixed)
FT_Sin(FT_Angle angle)
{
    return FT_Cos(FT_ANGLE_PI2 - angle);
}


/* documentation is in fttrigon.h */

FT_EXPORT_DEF(FT_Fixed)
FT_Tan(FT_Angle angle)
{
    FT_Vector v;


    v.x = FT_TRIG_COSCALE >> 2;
    v.y = 0;
    ft_trig_pseudo_rotate(&v, angle);

    return FT_DivFix(v.y, v.x);
}


/* documentation is in fttrigon.h */

FT_EXPORT_DEF(FT_Angle)
FT_Atan2(FT_Fixed dx,
         FT_Fixed dy)
{
    FT_Vector v;


    if (dx == 0 && dy == 0)
        return 0;

    v.x = dx;
    v.y = dy;
    ft_trig_prenorm(&v);
    ft_trig_pseudo_polarize(&v);

    return v.y;
}


/* documentation is in fttrigon.h */

FT_EXPORT_DEF(void)
FT_Vector_Unit(FT_Vector * vec,
               FT_Angle angle)
{
    vec->x = FT_TRIG_COSCALE >> 2;
    vec->y = 0;
    ft_trig_pseudo_rotate(vec, angle);
    vec->x >>= 12;
    vec->y >>= 12;
}


/* these macros return 0 for positive numbers,
   and -1 for negative ones */
#define FT_SIGN_LONG(x)   ((x) >> (FT_SIZEOF_LONG * 8 - 1))
#define FT_SIGN_INT(x)    ((x) >> (FT_SIZEOF_INT * 8 - 1))
#define FT_SIGN_INT32(x)  ((x) >> 31)
#define FT_SIGN_INT16(x)  ((x) >> 15)


/* documentation is in fttrigon.h */

FT_EXPORT_DEF(void)
FT_Vector_Rotate(FT_Vector * vec,
                 FT_Angle angle)
{
    FT_Int shift;
    FT_Vector v;


    v.x = vec->x;
    v.y = vec->y;

    if (angle && (v.x != 0 || v.y != 0))
    {
        shift = ft_trig_prenorm(&v);
        ft_trig_pseudo_rotate(&v, angle);
        v.x = ft_trig_downscale(v.x);
        v.y = ft_trig_downscale(v.y);

        if (shift > 0)
        {
            FT_Int32 half = (FT_Int32)1L << (shift - 1);


            vec->x = (v.x + half + FT_SIGN_LONG(v.x)) >> shift;
            vec->y = (v.y + half + FT_SIGN_LONG(v.y)) >> shift;
        }
        else
        {
            shift = -shift;
            vec->x = v.x << shift;
            vec->y = v.y << shift;
        }
    }
}


/* documentation is in fttrigon.h */

FT_EXPORT_DEF(FT_Fixed)
FT_Vector_Length(FT_Vector * vec)
{
    FT_Int shift;
    FT_Vector v;


    v = *vec;

    /* handle trivial cases */
    if (v.x == 0)
    {
        return (v.y >= 0) ? v.y : -v.y;
    }
    else if (v.y == 0)
    {
        return (v.x >= 0) ? v.x : -v.x;
    }

    /* general case */
    shift = ft_trig_prenorm(&v);
    ft_trig_pseudo_polarize(&v);

    v.x = ft_trig_downscale(v.x);

    if (shift > 0)
        return (v.x + (1 << (shift - 1))) >> shift;

    return v.x << -shift;
}


/* documentation is in fttrigon.h */

FT_EXPORT_DEF(void)
FT_Vector_Polarize(FT_Vector * vec,
                   FT_Fixed * length,
                   FT_Angle * angle)
{
    FT_Int shift;
    FT_Vector v;


    v = *vec;

    if (v.x == 0 && v.y == 0)
        return;

    shift = ft_trig_prenorm(&v);
    ft_trig_pseudo_polarize(&v);

    v.x = ft_trig_downscale(v.x);

    *length = (shift >= 0) ? (v.x >> shift) : (v.x << -shift);
    *angle = v.y;
}


/* documentation is in fttrigon.h */

FT_EXPORT_DEF(void)
FT_Vector_From_Polar(FT_Vector * vec,
                     FT_Fixed length,
                     FT_Angle angle)
{
    vec->x = length;
    vec->y = 0;

    FT_Vector_Rotate(vec, angle);
}


/* documentation is in fttrigon.h */

FT_EXPORT_DEF(FT_Angle)
FT_Angle_Diff(FT_Angle angle1,
              FT_Angle angle2)
{
    FT_Angle delta = angle2 - angle1;


    delta %= FT_ANGLE_2PI;
    if (delta < 0)
        delta += FT_ANGLE_2PI;

    if (delta > FT_ANGLE_PI)
        delta -= FT_ANGLE_2PI;

    return delta;
}


/* END */